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## Geng, Xianguo

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 Author ID: geng.xianguo Published as: Geng, X. G.; Geng, Xian Guo; Geng, Xian-Guo; Geng, Xiangguo; Geng, Xianguo External Links: ResearchGate · dblp
 Documents Indexed: 182 Publications since 1988 Reviewing Activity: 32 Reviews
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#### Co-Authors

 12 single-authored 27 Xue, Bo 19 Dai, Huihui 17 He, Guoliang 17 Wu, Lihua 14 Cao, Cewen 12 Wu, Yongtang 12 Zeng, Xin 11 Wei, Jiao 10 Li, Ruomeng 10 Zhu, Junyi 8 Zhai, Yunyun 5 Liu, Huan 5 Shen, Jing 5 Su, Ting 5 Wu, Jianping 4 Chen, Jinbing 4 Chen, Mingming 4 Gong, Dong 4 Ma, Yunling 4 Wang, Hui 4 Wang, Kedong 4 Wu, Jingzhu 4 Xing, Xiuzhi 3 Guan, Liang 3 Ma, Wen-Xiu 2 Hu, Xingbiao 2 Li, Xuemei 2 Li, Zhu 2 Nie, Hui 1 Cao, Cen 1 Cao, Clewen 1 Chao, Ying 1 Dai, Hui-Hui 1 Du, Dianlou 1 Duan, Jinqiao 1 Fan, Engui 1 Li, Fang 1 Li, Fang 1 Li, Fang 1 Li, Yihao 1 Liu, Wei 1 Lv, Yanyan 1 Mu, Weihua 1 Tam, Honwah 1 Wang, Hongye 1 Wang, Junmin 1 Wang, Linlin 1 Wang, Xin 1 Wang, Xin 1 Wang, Xin 1 Xu, Taixi 1 Ye, Xiaofeng 1 Zhang, Jinshun 1 Zhu, Siming
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#### Serials

 19 Journal of Mathematical Physics 11 Chaos, Solitons and Fractals 9 Physics Letters. A 8 Journal of the Physical Society of Japan 7 Applied Mathematics Letters 7 Journal of Physics A: Mathematical and General 7 Journal of Nonlinear Mathematical Physics 7 Communications in Theoretical Physics 6 Journal of Mathematical Analysis and Applications 6 Applied Mathematics and Computation 6 Communications in Nonlinear Science and Numerical Simulation 5 Mathematical Methods in the Applied Sciences 5 Journal of Geometry and Physics 4 Wave Motion 4 Studies in Applied Mathematics 3 Theoretical and Mathematical Physics 3 Acta Mathematicae Applicatae Sinica 3 Chinese Annals of Mathematics. Series A 3 Journal of Nonlinear Science 2 Modern Physics Letters B 2 IMA Journal of Applied Mathematics 2 Nonlinearity 2 Physica A 2 Advances in Mathematics 2 Annals of Physics 2 Acta Mathematica Scientia 2 Mathematical Physics, Analysis and Geometry 2 International Journal of Geometric Methods in Modern Physics 2 Journal of Physics A: Mathematical and Theoretical 2 Analysis and Mathematical Physics 1 International Journal of Modern Physics B 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Physics Letters. B 1 Reports on Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Reviews in Mathematical Physics 1 Acta Mathematica Sinica 1 Journal of Differential Equations 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Results in Mathematics 1 Transactions of the American Mathematical Society 1 Acta Applicandae Mathematicae 1 Physica D 1 Annals of Differential Equations 1 IMRN. International Mathematics Research Notices 1 SIAM Journal on Mathematical Analysis 1 Acta Mathematica Sinica. New Series 1 Chinese Science Bulletin 1 Applied Mathematics 1 Nonlinear Dynamics 1 Journal of Zhengzhou University. Natural Science Edition 1 Chinese Quarterly Journal of Mathematics 1 Annales Henri Poincaré 1 Journal of Applied Mathematics 1 Acta Physica Polonica B 1 Journal of Xuzhou Normal University. Natural Science Edition 1 Analysis and Applications (Singapore) 1 Journal of Mathematical Physics, Analysis, Geometry 1 Frontiers of Mathematics in China 1 International Journal of Applied Mathematics and Applications 1 Advances in Mathematical Physics 1 East Asian Journal on Applied Mathematics
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#### Fields

 140 Dynamical systems and ergodic theory (37-XX) 133 Partial differential equations (35-XX) 28 Algebraic geometry (14-XX) 9 Ordinary differential equations (34-XX) 6 Numerical analysis (65-XX) 4 Difference and functional equations (39-XX) 4 Mechanics of particles and systems (70-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Fluid mechanics (76-XX) 2 Operator theory (47-XX) 2 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX)

#### Citations contained in zbMATH Open

144 Publications have been cited 1,380 times in 702 Documents Cited by Year
Relation between the Kadomtsev-Petviashvili equation and the confocal involutive system. Zbl 0947.35138
Cao, Cewen; Wu, Yongtang; Geng, Xianguo
1999
An extension of integrable peakon equations with cubic nonlinearity. Zbl 1171.37331
Geng, Xianguo; Xue, Bo
2009
A generalized Hirota-Satsuma coupled Korteweg-de Vries equation and Miura transformations. Zbl 0935.37029
Wu, Yongtang; Geng, Xianguo; Hu, Xingbiao; Zhu, Siming
1999
Decomposition of the $$(2+1)$$-dimensional Gardner equation and its quasi-periodic solutions. Zbl 1160.37405
Geng, Xianguo; Cao, Cewen
2001
C. Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy. Zbl 0719.35082
Cao, Cewen; Geng, Xianguo
1990
A new hierarchy of integrable differential-difference equations and Darboux transformation. Zbl 0931.35190
Wu, Yongtang; Geng, Xianguo
1998
Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations. Zbl 1039.37061
Geng, Xianguo
2003
$$N$$-soliton solution and its Wronskian form of a $$(3+1)$$-dimensional nonlinear evolution equation. Zbl 1209.35116
Geng, Xianguo; Ma, Yunling
2007
A new integrable symplectic map associated with lattice soliton equations. Zbl 0864.58028
Wu, Yongtang; Geng, Xianguo
1996
Quasi-periodic solutions of the modified Kadomtsev-Petviashvili equation. Zbl 0941.35090
Geng, Xianguo; Wu, Yongtang; Cao, Cewen
1999
From the special $$2+1$$ Toda lattice to the Kadomtsev-Petviashvili equation. Zbl 0977.37036
Cao, Cewen; Geng, Xianguo; Wu, Yongtang
1999
Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy. Zbl 1304.37046
Geng, Xianguo; Zhai, Yunyun; Dai, H. H.
2014
A three-component generalization of Camassa-Holm equation with $$N$$-peakon solutions. Zbl 1207.35254
Geng, Xianguo; Xue, Bo
2011
Algebro-geometric solution of the $$2+1$$ dimensional Burgers equation with a discrete variable. Zbl 1052.37050
Cao, Cewen; Geng, Xianguo; Wang, Hongye
2002
Darboux transformation and soliton solutions for generalized nonlinear Schrödinger equations. Zbl 0944.35093
Geng, Xianguo; Tam, Hon-Wah
1999
Algebro-geometric constructions of the modified Boussinesq flows and quasi-periodic solutions. Zbl 1223.37093
Geng, Xianguo; Wu, Lihua; He, Guoliang
2011
Bäcklund transformations of soliton systems from symmetry constraints. Zbl 1010.37048
Ma, Wen-Xiu; Geng, Xianguo
2001
The nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schrödinger equation. Zbl 1390.35325
Geng, Xianguo; Liu, Huan
2018
Initial-boundary value problems for the coupled nonlinear Schrödinger equation on the half-line. Zbl 1338.35408
Geng, Xianguo; Liu, Huan; Zhu, Junyi
2015
Quasi-periodic solutions for some $$(2+1)$$-dimensional integrable models generated by the Jaulent-Miodek hierarchy. Zbl 0978.37054
Geng, Xianguo; Cao, Cewen; Dai, H. H.
2001
A nonconfocal generator of involutive systems and three associated soliton hierarchies. Zbl 0737.35083
Cao, Cewen; Geng, Xianguo
1991
Riemann-Hilbert approach and $$N$$-soliton solutions for a generalized sasa-Satsuma equation. Zbl 07064143
Geng, Xianguo; Wu, Jianping
2016
Quasi-periodic solutions of the Kaup-Kupershmidt hierarchy. Zbl 1309.37070
Geng, Xianguo; Wu, Lihua; He, Guoliang
2013
Classical integrable systems generated through nonlinearization of eigenvalue problems. Zbl 0728.70012
Cao, Cewen; Geng, Xianguo
1990
Darboux transformation for an integrable generalization of the nonlinear Schrödinger equation. Zbl 1263.35196
Geng, Xianguo; Lv, Yanyan
2012
Finite-band solutions of the classical Boussinesq-Burgers equations. Zbl 0944.35085
Geng, Xianguo; Wu, Yongtang
1999
Quasi-periodic solutions of mixed AKNS equations. Zbl 1200.35016
Geng, Xianguo; Xue, Bo
2010
Nonlinearization of the Lax pairs for discrete Ablowitz-Ladik hierarchy. Zbl 1111.39011
Geng, Xianguo; Dai, H. H.
2007
Algebro-geometric constructions of the discrete Ablowitz-Ladik flows and applications. Zbl 1062.37092
Geng, Xianguo; Dai, H. H.; Cao, Cewen
2003
Finite-dimensional discrete systems and integrable systems through nonlinearization of the discrete eigenvalue problem. Zbl 0784.58048
Geng, Xianguo
1993
Algebro-geometric quasi-periodic solutions to the three-wave resonant interaction hierarchy. Zbl 1319.35211
He, Guoliang; Geng, Xianguo; Wu, Lihua
2014
A new super-extension of the KdV hierarchy. Zbl 1190.35197
Geng, Xianguo; Wu, Lihua
2010
Soliton solutions and quasiperiodic solutions of modified Korteweg-de Vries type equations. Zbl 1311.35255
Geng, Xianguo; Xue, Bo
2010
A finite-dimensional integrable system associated with the three-wave interaction equations. Zbl 0955.37034
Wu, Yongtang; Geng, Xianguo
1999
Initial-boundary problems for the vector modified Korteweg-de Vries equation via Fokas unified transform method. Zbl 1342.35306
Liu, Huan; Geng, Xianguo
2016
Quasi-periodic solutions of the $$2+1$$ dimensional modified Korteweg-de Vries equation. Zbl 0937.35155
Geng, Xianguo; Cao, Cewen
1999
Darboux transformation of the discrete Ablowitz-Ladik eigenvalue problem. Zbl 0693.65091
Geng, Xianguo
1989
The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices. Zbl 1403.37078
Wei, Jiao; Geng, Xianguo; Zeng, Xin
2019
The Deift-Zhou steepest descent method to long-time asymptotics for the Sasa-Satsuma equation. Zbl 1414.35137
Liu, Huan; Geng, Xianguo; Xue, Bo
2018
A hierarchy of coupled evolution equations with self-consistent sources and the dressing method. Zbl 1275.37034
Zhu, Junyi; Geng, Xianguo
2013
A super Camassa-Holm equation with $$N$$-peakon solutions. Zbl 1282.35284
Geng, Xianguo; Xue, Bo; Wu, Lihua
2013
Grammian determinant solution and Pfaffianization for a $$(3+1)$$-dimensional soliton equation. Zbl 1183.35237
Wu, Jian-Ping; Geng, Xian-Guo
2009
Explicit solutions of the $$2+1$$-dimensional modified Toda lattice through straightening out of the relativistic Toda flows. Zbl 1071.37052
Dai, H. H.; Geng, Xianguo
2003
Quasi-periodic solutions for some $$2+1$$-dimensional discrete models. Zbl 1008.70011
Geng, Xianguo; Dai, H. H.
2003
New completely integrable Neumann systems related to the perturbation KdV hierarchy. Zbl 0964.37043
Ma, Wen-Xiu; Geng, Xianguo
2000
A new integrable symplectic map of Neumann type. Zbl 0955.37030
Wu, Yongtang; Geng, Xianguo
1999
A vector general nonlinear Schrödinger equation with $$(m+n)$$ components. Zbl 1437.35627
Geng, Xianguo; Li, Ruomeng; Xue, Bo
2020
The AB equations and the $$\bar\partial$$-dressing method in semi-characteristic coordinates. Zbl 1302.37044
Zhu, Junyi; Geng, Xianguo
2014
Straightening out of the flows for the Hu hierarchy and its algebro-geometric solutions. Zbl 1256.35043
Zhai, Yunyun; Geng, Xianguo
2013
Explicit solutions of the $$2+1$$-dimensional breaking soliton equation. Zbl 1062.35103
Geng, Xianguo; Cao, Cewen
2004
Algebro-geometric solutions of $$(2+1)$$-dimensional coupled modified Kadomtsev-Petviashvili equations. Zbl 0991.37045
Geng, Xianguo; Dai, H. H.
2000
Hirota bilinear approach to a new integrable differential-difference system. Zbl 0944.35101
Hu, Xing-Biao; Wu, Yong-Tang; Geng, Xian-Guo
1999
The Hamiltonian structure and new finite-dimensional integrable system associated with Harry-Dym type equations. Zbl 0961.35506
Geng, Xian Guo
1994
Rogue periodic waves of the sine-Gordon equation. Zbl 1440.35030
Li, Ruomeng; Geng, Xianguo
2020
Trace formula and new form of $$N$$-soliton to the Gerdjikov-Ivanov equation. Zbl 1402.35068
Nie, Hui; Zhu, Junyi; Geng, Xianguo
2018
Novel Wronskian condition and new exact solutions to a $$(3+1)$$-dimensional generalized KP equation. Zbl 1284.35384
Wu, Jian-Ping; Geng, Xian-Guo
2013
A super extension of Kaup-Newell hierarchy. Zbl 1222.37052
Geng, Xian-Guo; Wu, Li-Hua
2010
Two hierarchies of new nonlinear evolution equations associated with $$3 \times 3$$ matrix spectral problems. Zbl 1142.37358
Geng, Xianguo; Du, Dianlou
2006
Lax matrix and a generalized coupled KdV hierarchy. Zbl 1098.35562
Li, Xuemei; Geng, Xianguo
2003
Nonlinearization of the $$3\times 3$$ matrix eigenvalue problem related to coupled nonlinear Schrödinger equations. Zbl 0924.35149
Geng, X. G.; Dai, H. H.
1999
A new nonlinear wave equation: Darboux transformation and soliton solutions. Zbl 07213988
Geng, Xianguo; Shen, Jing; Xue, Bo
2018
Algebro-geometric solutions to the Manakov hierarchy. Zbl 1338.35384
Wu, Lihua; Geng, Xianguo; He, Guoliang
2016
The full positive flows of Manakov hierarchy, Hamiltonian structures and conservation laws. Zbl 1329.35294
Wu, Lihua; He, Guoliang; Geng, Xianguo
2013
Algebro-geometric solutions of the TD hierarchy. Zbl 1303.37023
Geng, Xianguo; Zeng, Xin; Xue, Bo
2013
Darboux and Bäcklund transformations of the bidirectional Sawada-Kotera equation. Zbl 1247.37079
Ma, Yunling; Geng, Xianguo
2012
Decomposition to the modified Jaulent-Miodek hierarchy. Zbl 1142.37356
Chen, Jinbing; Geng, Xianguo
2006
Decomposition of a $$2 + 1$$-dimensional Volterra type lattice and its quasi-periodic solutions. Zbl 1069.37061
Dai, H. H.; Geng, Xianguo
2003
A multipotential generalization of the nonlinear diffusion equation. Zbl 1058.37523
Geng, Xianguo; Ma, Wen-Xiu
2000
New finite-dimensional completely integrable systems associated with the sine-Gordon equation. Zbl 0942.37047
Dai, Hui-Hui; Geng, Xianguo
1999
Riemann theta function solutions of the Caudrey-Dodd-Gibbon-Sawada-Kotera hierarchy. Zbl 1415.37089
Geng, Xianguo; He, Guoliang; Wu, Lihua
2019
Quasi-periodic solutions to the two-component nonlinear Klein-Gordon equation. Zbl 1277.35299
Wu, Lihua; He, Guoliang; Geng, Xianguo
2013
$$N$$-soliton and quasi-periodic solutions of the KdV6 equations. Zbl 1311.35254
Geng, Xianguo; Xue, Bo
2012
Some new integrable nonlinear evolution equations and Darboux transformation. Zbl 1309.37072
Geng, Xianguo; He, Guoliang
2010
Darboux transformation and explicit solutions for the Satsuma-Hirota coupled equation. Zbl 1195.35260
Geng, Xianguo; He, Guoliang
2010
Algebro-geometric constructions of the $$(2+1)$$-dimensional differential-difference equation. Zbl 1209.37085
Zhu, Junyi; Geng, Xianguo
2007
A hierarchy of new nonlinear differential-difference equations. Zbl 1223.34037
Geng, Xianguo; Dai, Huihui
2006
A new Neumann type integrable system related to the coupled Harry-Dym hierarchy. Zbl 1145.37326
Chen, Jinbing; Geng, Xianguo
2005
Decomposition and straightening out of the coupled mixed nonlinear Schrödinger flows. Zbl 1045.37038
Geng, Xianguo; Dai, H. H.
2004
Explicit solutions of some (2+1)-dimensional differential-difference equations. Zbl 1028.35155
Wang, Junmin; Geng, Xianguo
2003
Involutive solutions for Toda and Langmuir lattices through nonlinearization of Lax pairs. Zbl 0749.35038
Geng, Xianguo
1992
Long-time asymptotics of the coupled modified Korteweg-de Vries equation. Zbl 1420.35313
Geng, Xianguo; Chen, Mingming; Wang, Kedong
2019
Inverse scattering transform of the coupled Sasa-Satsuma equation by Riemann-Hilbert approach. Zbl 1365.35167
Wu, Jian-Ping; Geng, Xian-Guo
2017
Quasi-periodic solutions to the hierarchy of four-component Toda lattices. Zbl 1339.37061
Wei, Jiao; Geng, Xianguo; Zeng, Xin
2016
A vector generalization of Volterra type differential-difference equations. Zbl 1351.39008
Wei, Jiao; Geng, Xianguo
2016
Darboux transformation of the Drinfeld-Sokolov-Satsuma-Hirota system and exact solutions. Zbl 1360.37168
Geng, Xianguo; Li, Ruomeng
2015
Generalized bilinear differential operators application in a $$(3+1)$$-dimensional generalized shallow water equation. Zbl 1342.35270
Wu, Jingzhu; Xing, Xiuzhi; Geng, Xianguo
2015
A new integrable equation with peakons and cuspons and its bi-Hamiltonian structure. Zbl 1326.35066
Geng, Xianguo; Li, Ruomeng; Xue, Bo
2015
Explicit quasi-periodic solutions of the Kaup-Newell hierarchy. Zbl 1317.37088
Geng, Xianguo; Li, Zhu; Xue, Bo; Guan, Liang
2015
Coupled Camassa-Holm equations, $$N$$-peakons and infinitely many conservation laws. Zbl 1284.35337
Geng, Xianguo; Wang, Hui
2013
A generalization of Toda lattices and their bi-Hamiltonian structures. Zbl 1263.82009
Geng, Xianguo; Li, Fang; Xue, Bo
2012
Quasi-periodic solutions of nonlinear evolution equations associated with a $$3 \times 3$$ matrix spectral problem. Zbl 1243.37058
Geng, Xianguo; Wu, Lihua; He, Guoliang
2011
On the application of a generalized dressing method to the integration of variable-coefficient coupled Hirota equations. Zbl 1304.37053
Su, Ting; Dai, Hui-Hui; Geng, Xianguo
2009
Algebro-geometric solution to the modified Kadomtsev-Petviashvili equation. Zbl 1079.35089
Chen, Jinbing; Geng, Xianguo
2005
Finite-dimensional integrable systems through the decomposition of a modified Boussinesq equation. Zbl 1059.37039
Dai, H.-H.; Geng, Xianguo
2003
Decomposition of certain nonlinear evolution equations and their quasi-periodic solutions. Zbl 1162.37324
Dai, H.-H.; Geng, Xianguo
2002
On the decomposition of the modified Kadomtsev-Petviashvili equation and explicit solutions. Zbl 0972.35133
Dai, H. H.; Geng, Xianguo
2000
A Hermitian symmetric space Fokas-Lenells equation: solitons, breathers, rogue waves. Zbl 1414.35194
Geng, Xianguo; Shen, Jing; Xue, Bo
2019
Exact solutions of a negative matrix AKNS system with a Hermitian symmetric space. Zbl 1410.35181
Shen, Jing; Geng, Xianguo; Xue, Bo
2019
Periodic and rational solutions of the reduced Maxwell-Bloch equations. Zbl 07263324
Wei, Jiao; Wang, Xin; Geng, Xianguo
2018
Riemann-Hilbert approach to TD equation with nonzero boundary condition. Zbl 1402.35195
Zhu, Junyi; Wang, Linlin; Geng, Xianguo
2018
A vector general nonlinear Schrödinger equation with $$(m+n)$$ components. Zbl 1437.35627
Geng, Xianguo; Li, Ruomeng; Xue, Bo
2020
Rogue periodic waves of the sine-Gordon equation. Zbl 1440.35030
Li, Ruomeng; Geng, Xianguo
2020
On a vector long wave-short wave-type model. Zbl 1454.35314
Li, Ruomeng; Geng, Xianguo
2020
Darboux transformations for a matrix long-wave-short-wave equation and higher-order rational rogue-wave solutions. Zbl 1446.35163
Li, Ruomeng; Geng, Xianguo; Xue, Bo
2020
The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices. Zbl 1403.37078
Wei, Jiao; Geng, Xianguo; Zeng, Xin
2019
Riemann theta function solutions of the Caudrey-Dodd-Gibbon-Sawada-Kotera hierarchy. Zbl 1415.37089
Geng, Xianguo; He, Guoliang; Wu, Lihua
2019
Long-time asymptotics of the coupled modified Korteweg-de Vries equation. Zbl 1420.35313
Geng, Xianguo; Chen, Mingming; Wang, Kedong
2019
A Hermitian symmetric space Fokas-Lenells equation: solitons, breathers, rogue waves. Zbl 1414.35194
Geng, Xianguo; Shen, Jing; Xue, Bo
2019
Exact solutions of a negative matrix AKNS system with a Hermitian symmetric space. Zbl 1410.35181
Shen, Jing; Geng, Xianguo; Xue, Bo
2019
Dynamical behaviour of rogue wave solutions in a multi-component AB system. Zbl 07222033
Geng, Xianguo; Shen, Jing; Xue, Bo
2019
A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation. Zbl 1417.37252
Geng, Xianguo; Zhai, Yunyun; Xue, Bo; Wei, Jiao
2019
The nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schrödinger equation. Zbl 1390.35325
Geng, Xianguo; Liu, Huan
2018
The Deift-Zhou steepest descent method to long-time asymptotics for the Sasa-Satsuma equation. Zbl 1414.35137
Liu, Huan; Geng, Xianguo; Xue, Bo
2018
Trace formula and new form of $$N$$-soliton to the Gerdjikov-Ivanov equation. Zbl 1402.35068
Nie, Hui; Zhu, Junyi; Geng, Xianguo
2018
A new nonlinear wave equation: Darboux transformation and soliton solutions. Zbl 07213988
Geng, Xianguo; Shen, Jing; Xue, Bo
2018
Periodic and rational solutions of the reduced Maxwell-Bloch equations. Zbl 07263324
Wei, Jiao; Wang, Xin; Geng, Xianguo
2018
Riemann-Hilbert approach to TD equation with nonzero boundary condition. Zbl 1402.35195
Zhu, Junyi; Wang, Linlin; Geng, Xianguo
2018
The vector derivative nonlinear Schrödinger equation on the half-line. Zbl 1406.35364
Liu, Huan; Geng, Xianguo
2018
$$N$$ solutions for a derivative nonlinear Schrödinger-type equation via Riemann-Hilbert approach. Zbl 1391.35305
Geng, Xianguo; Nie, Hui
2018
Inverse scattering transform of the coupled Sasa-Satsuma equation by Riemann-Hilbert approach. Zbl 1365.35167
Wu, Jian-Ping; Geng, Xian-Guo
2017
Application of the trigonal curve to the Blaszak-Marciniak lattice hierarchy. Zbl 1382.37076
Geng, Xianguo; Zeng, Xin
2017
Quasi-periodic solutions of the Belov-Chaltikian lattice hierarchy. Zbl 1408.37123
Geng, Xianguo; Zeng, Xin
2017
$$N$$-soliton solution and soliton resonances for the $$(2+1)$$-dimensional inhomogeneous Gardner equation. Zbl 1375.35465
Wang, Xin; Geng, Xian-Guo
2017
The coupled Sasa-Satsuma hierarchy: trigonal curve and finite genus solutions. Zbl 1376.37113
Zhai, Yunyun; Geng, Xianguo
2017
Riemann-Hilbert approach and $$N$$-soliton solutions for a generalized sasa-Satsuma equation. Zbl 07064143
Geng, Xianguo; Wu, Jianping
2016
Initial-boundary problems for the vector modified Korteweg-de Vries equation via Fokas unified transform method. Zbl 1342.35306
Liu, Huan; Geng, Xianguo
2016
Algebro-geometric solutions to the Manakov hierarchy. Zbl 1338.35384
Wu, Lihua; Geng, Xianguo; He, Guoliang
2016
Quasi-periodic solutions to the hierarchy of four-component Toda lattices. Zbl 1339.37061
Wei, Jiao; Geng, Xianguo; Zeng, Xin
2016
A vector generalization of Volterra type differential-difference equations. Zbl 1351.39008
Wei, Jiao; Geng, Xianguo
2016
Algebro-geometric constructions of the Wadati-Konno-Ichikawa flows and applications. Zbl 1337.37055
Li, Zhu; Geng, Xianguo; Guan, Liang
2016
Initial-boundary value problems for the coupled nonlinear Schrödinger equation on the half-line. Zbl 1338.35408
Geng, Xianguo; Liu, Huan; Zhu, Junyi
2015
Darboux transformation of the Drinfeld-Sokolov-Satsuma-Hirota system and exact solutions. Zbl 1360.37168
Geng, Xianguo; Li, Ruomeng
2015
Generalized bilinear differential operators application in a $$(3+1)$$-dimensional generalized shallow water equation. Zbl 1342.35270
Wu, Jingzhu; Xing, Xiuzhi; Geng, Xianguo
2015
A new integrable equation with peakons and cuspons and its bi-Hamiltonian structure. Zbl 1326.35066
Geng, Xianguo; Li, Ruomeng; Xue, Bo
2015
Explicit quasi-periodic solutions of the Kaup-Newell hierarchy. Zbl 1317.37088
Geng, Xianguo; Li, Zhu; Xue, Bo; Guan, Liang
2015
A hierarchy of new nonlinear evolution equations and generalized bi-Hamiltonian structures. Zbl 1410.35189
Wei, Jiao; Geng, Xianguo
2015
Algebro-geometric solution to the Bullough-Dodd-Zhiber-Shabat equation. Zbl 1315.35184
Wu, Lihua; Geng, Xianguo; Zhang, Jinshun
2015
A note on the quasi-periodic solutions of the modified Boussinesq hierarchy. Zbl 1321.35191
Wu, Lihua; He, Guoliang; Geng, Xianguo
2015
Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy. Zbl 1304.37046
Geng, Xianguo; Zhai, Yunyun; Dai, H. H.
2014
Algebro-geometric quasi-periodic solutions to the three-wave resonant interaction hierarchy. Zbl 1319.35211
He, Guoliang; Geng, Xianguo; Wu, Lihua
2014
The AB equations and the $$\bar\partial$$-dressing method in semi-characteristic coordinates. Zbl 1302.37044
Zhu, Junyi; Geng, Xianguo
2014
Algebro-geometric solutions of the discrete Ragnisco-Tu hierarchy. Zbl 1417.37247
Zeng, Xin; Geng, Xianguo
2014
Quasiperiodic solutions of the discrete Chen-Lee-Liu hierarchy. Zbl 1310.37038
Zeng, Xin; Geng, Xianguo
2014
Explicit quasi-periodic solutions of the Vakhnenko equation. Zbl 1304.35045
Zhai, Yunyun; Geng, Xianguo; He, Guoliang
2014
Quasi-periodic solutions of the Kaup-Kupershmidt hierarchy. Zbl 1309.37070
Geng, Xianguo; Wu, Lihua; He, Guoliang
2013
A hierarchy of coupled evolution equations with self-consistent sources and the dressing method. Zbl 1275.37034
Zhu, Junyi; Geng, Xianguo
2013
A super Camassa-Holm equation with $$N$$-peakon solutions. Zbl 1282.35284
Geng, Xianguo; Xue, Bo; Wu, Lihua
2013
Straightening out of the flows for the Hu hierarchy and its algebro-geometric solutions. Zbl 1256.35043
Zhai, Yunyun; Geng, Xianguo
2013
Novel Wronskian condition and new exact solutions to a $$(3+1)$$-dimensional generalized KP equation. Zbl 1284.35384
Wu, Jian-Ping; Geng, Xian-Guo
2013
The full positive flows of Manakov hierarchy, Hamiltonian structures and conservation laws. Zbl 1329.35294
Wu, Lihua; He, Guoliang; Geng, Xianguo
2013
Algebro-geometric solutions of the TD hierarchy. Zbl 1303.37023
Geng, Xianguo; Zeng, Xin; Xue, Bo
2013
Quasi-periodic solutions to the two-component nonlinear Klein-Gordon equation. Zbl 1277.35299
Wu, Lihua; He, Guoliang; Geng, Xianguo
2013
Coupled Camassa-Holm equations, $$N$$-peakons and infinitely many conservation laws. Zbl 1284.35337
Geng, Xianguo; Wang, Hui
2013
A super hierarchy of the vector nonlinear Schrödinger equations and Hamiltonian structures, conservation laws. Zbl 1298.37050
He, Guoliang; Zhai, Yunyun; Geng, Xianguo
2013
Quasi-periodic solutions of the discrete mKdV hierarchy. Zbl 1282.35331
Geng, Xianguo; Gong, Dong
2013
Quasi-periodic solutions of coupled KdV type equations. Zbl 1420.37093
Xue, Bo; Li, Fang; Geng, Xianguo
2013
Darboux transformation for an integrable generalization of the nonlinear Schrödinger equation. Zbl 1263.35196
Geng, Xianguo; Lv, Yanyan
2012
Darboux and Bäcklund transformations of the bidirectional Sawada-Kotera equation. Zbl 1247.37079
Ma, Yunling; Geng, Xianguo
2012
$$N$$-soliton and quasi-periodic solutions of the KdV6 equations. Zbl 1311.35254
Geng, Xianguo; Xue, Bo
2012
A generalization of Toda lattices and their bi-Hamiltonian structures. Zbl 1263.82009
Geng, Xianguo; Li, Fang; Xue, Bo
2012
Algebro-geometric solutions to the modified Sawada-Kotera hierarchy. Zbl 1284.37053
Wu, Lihua; He, Guoliang; Geng, Xianguo
2012
Quasiperiodic solutions of Jaulent-Miodek equations with a negative flow. Zbl 1297.37036
Xue, Bo; Geng, Xianguo; Li, Fang
2012
Quasi-periodic solutions of the relativistic Toda hierarchy. Zbl 1282.37035
Gong, Dong; Geng, Xianguo
2012
On the application of a generalized version of the dressing method to the integration of variable coefficient $$N$$-coupled nonlinear Schrödinger equation. Zbl 1308.35285
Su, Ting; Dai, Huihui; Geng, Xian Guo
2012
A three-component generalization of Camassa-Holm equation with $$N$$-peakon solutions. Zbl 1207.35254
Geng, Xianguo; Xue, Bo
2011
Algebro-geometric constructions of the modified Boussinesq flows and quasi-periodic solutions. Zbl 1223.37093
Geng, Xianguo; Wu, Lihua; He, Guoliang
2011
Quasi-periodic solutions of nonlinear evolution equations associated with a $$3 \times 3$$ matrix spectral problem. Zbl 1243.37058
Geng, Xianguo; Wu, Lihua; He, Guoliang
2011
Decomposition and straightening out of the discrete Kaup-Newell flows. Zbl 1247.37057
Geng, Xianguo; Su, Ting
2011
Quasi-periodic solutions of mixed AKNS equations. Zbl 1200.35016
Geng, Xianguo; Xue, Bo
2010
A new super-extension of the KdV hierarchy. Zbl 1190.35197
Geng, Xianguo; Wu, Lihua
2010
Soliton solutions and quasiperiodic solutions of modified Korteweg-de Vries type equations. Zbl 1311.35255
Geng, Xianguo; Xue, Bo
2010
A super extension of Kaup-Newell hierarchy. Zbl 1222.37052
Geng, Xian-Guo; Wu, Li-Hua
2010
Some new integrable nonlinear evolution equations and Darboux transformation. Zbl 1309.37072
Geng, Xianguo; He, Guoliang
2010
Darboux transformation and explicit solutions for the Satsuma-Hirota coupled equation. Zbl 1195.35260
Geng, Xianguo; He, Guoliang
2010
Algebro-geometric constructions of semi-discrete Chen-Lee-Liu equations. Zbl 1242.37053
Su, Ting; Geng, Xianguo; Dai, Huihui
2010
Darboux transformation and explicit solutions for Drinfel’d-Sokolov-Wilson equation. Zbl 1229.81074
Geng, Xian-Guo; Wu, Li-Hua
2010
Some new integrable nonlinear evolution equations and their infinitely many conservation laws. Zbl 1206.37041
Geng, Xianguo; Xue, Bo
2010
An extension of integrable peakon equations with cubic nonlinearity. Zbl 1171.37331
Geng, Xianguo; Xue, Bo
2009
Grammian determinant solution and Pfaffianization for a $$(3+1)$$-dimensional soliton equation. Zbl 1183.35237
Wu, Jian-Ping; Geng, Xian-Guo
2009
On the application of a generalized dressing method to the integration of variable-coefficient coupled Hirota equations. Zbl 1304.37053
Su, Ting; Dai, Hui-Hui; Geng, Xianguo
2009
A coupled nonlinear Schrödinger type equation and its explicit solutions. Zbl 1198.37093
Ma, Yunling; Geng, Xianguo
2009
Quasi-periodic solutions of soliton equations associated with third-order spectral problems through reduction. Zbl 1152.35100
Dai, H. H.; Geng, Xianguo; Fan, Engui
2008
$$N$$-soliton solution and its Wronskian form of a $$(3+1)$$-dimensional nonlinear evolution equation. Zbl 1209.35116
Geng, Xianguo; Ma, Yunling
2007
Nonlinearization of the Lax pairs for discrete Ablowitz-Ladik hierarchy. Zbl 1111.39011
Geng, Xianguo; Dai, H. H.
2007
Algebro-geometric constructions of the $$(2+1)$$-dimensional differential-difference equation. Zbl 1209.37085
Zhu, Junyi; Geng, Xianguo
2007
The generalized dressing method with applications to variable-coefficient coupled Kadomtsev-Petviashvili equations. Zbl 1139.35395
Zhu, Junyi; Geng, Xianguo
2007
Discrete coupled derivative nonlinear Schrödinger equations and their quasi-periodic solutions. Zbl 1106.35094
Geng, Xianguo; Su, Ting
2007
Two hierarchies of new nonlinear evolution equations associated with $$3 \times 3$$ matrix spectral problems. Zbl 1142.37358
Geng, Xianguo; Du, Dianlou
2006
Decomposition to the modified Jaulent-Miodek hierarchy. Zbl 1142.37356
Chen, Jinbing; Geng, Xianguo
2006
A hierarchy of new nonlinear differential-difference equations. Zbl 1223.34037
Geng, Xianguo; Dai, Huihui
2006
The generalized version of dressing method with applications to AKNS equations. Zbl 1110.35336
Zhu, Junyi; Geng, Xianguo
2006
A new Neumann type integrable system related to the coupled Harry-Dym hierarchy. Zbl 1145.37326
Chen, Jinbing; Geng, Xianguo
2005
Algebro-geometric solution to the modified Kadomtsev-Petviashvili equation. Zbl 1079.35089
Chen, Jinbing; Geng, Xianguo
2005
Explicit solutions of the $$2+1$$-dimensional breaking soliton equation. Zbl 1062.35103
Geng, Xianguo; Cao, Cewen
2004
Decomposition and straightening out of the coupled mixed nonlinear Schrödinger flows. Zbl 1045.37038
Geng, Xianguo; Dai, H. H.
2004
Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations. Zbl 1039.37061
Geng, Xianguo
2003
Algebro-geometric constructions of the discrete Ablowitz-Ladik flows and applications. Zbl 1062.37092
Geng, Xianguo; Dai, H. H.; Cao, Cewen
2003
Explicit solutions of the $$2+1$$-dimensional modified Toda lattice through straightening out of the relativistic Toda flows. Zbl 1071.37052
Dai, H. H.; Geng, Xianguo
2003
Quasi-periodic solutions for some $$2+1$$-dimensional discrete models. Zbl 1008.70011
Geng, Xianguo; Dai, H. H.
2003
Lax matrix and a generalized coupled KdV hierarchy. Zbl 1098.35562
Li, Xuemei; Geng, Xianguo
2003
...and 44 more Documents
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#### Cited by 719 Authors

 86 Geng, Xianguo 44 Ma, Wen-Xiu 36 Xu, Xixiang 24 Xue, Bo 23 Fan, Engui 19 Zhang, Yufeng 18 Qiao, Zhijun 17 Zhou, Ruguang 16 He, Guoliang 15 Yang, Hongxiang 14 Xia, Tie-Cheng 13 Wen, Xiaoyong 13 Zhu, Junyi 12 Dong, Huanhe 12 Du, Dianlou 12 Tian, Shoufu 12 Wu, Lihua 12 Zhang, Hongqing 11 Chen, Jinbing 11 Tian, Bo 11 Zeng, Xin 10 Chen, Dengyuan 10 Guo, Boling 10 Hu, Xingbiao 10 Lü, Xing 10 Wang, Dengshan 10 Wazwaz, Abdul-Majid Abdul-Rahman 10 Xia, Baoqiang 9 Li, Xinyue 9 Wei, Jiao 9 Yang, Xiao 9 Zhao, Qiulan 9 Zhaqilao, Z. 8 Dai, Huihui 8 Gao, Yitian 8 He, Jingsong 8 Li, Nianhua 8 Sun, Yepeng 8 Tam, Honwah 8 Yu, Fajun 7 Li, Ruomeng 7 Li, Zhu 7 Liu, Qingping 7 Wu, Yongtang 7 Xu, Tao 7 Zhang, Haiqiang 6 Biswas, Anjan 6 Chang, Xiangke 6 Cheng, Yi 6 Ding, Haiyong 6 Gepreel, Khaled A. 6 Hu, Beibei 6 Mi, Yongsheng 6 Yu, Jing 6 Zayed, Elsayed M. E. 6 Zhai, Yunyun 6 Zhang, Yi 5 Chen, Yong 5 Hon, Yiu-Chung 5 Ji, Jie 5 Khalique, Chaudry Masood 5 Qu, Changzheng 5 Su, Ting 5 Tang, Yaning 5 Wang, Lei 5 Yan, Zhenya 5 Yao, Yuqin 5 Zhang, Huiqun 5 Zhang, Jianbing 4 Cao, Cewen 4 Chen, Mingming 4 Jiang, Yan 4 Li, Hongmin 4 Li, Yuxia 4 Liu, Nan 4 Lou, Senyue 4 Mei, Jianqin 4 Mu, Chunlai 4 Shen, Shoufeng 4 Szmigielski, Jacek 4 Wang, Kedong 4 Wang, Xiubin 4 Wu, Jianping 4 Yang, Jin-Jie 4 Yong, Xuelin 4 Zhang, Dajun 4 Zhang, Ning 4 Zhang, Tiantian 4 Zhao, Haiqiong 4 Zhu, Zuonong 3 Belić, Milivoj R. 3 Cheng, Wenguang 3 Fan, Fangcheng 3 Gai, Xiaoling 3 Ganji, Davood Domiri 3 Gao, Binfang 3 Gong, Dong 3 Guan, Liang 3 Guo, Rui 3 Hou, Yu ...and 619 more Authors
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#### Cited in 109 Serials

 79 Journal of Mathematical Physics 63 Applied Mathematics and Computation 31 Applied Mathematics Letters 31 Nonlinear Dynamics 31 Communications in Nonlinear Science and Numerical Simulation 30 Chaos, Solitons and Fractals 25 Modern Physics Letters B 25 Journal of Mathematical Analysis and Applications 25 Journal of Nonlinear Mathematical Physics 22 International Journal of Modern Physics B 18 Physics Letters. A 14 Journal of Geometry and Physics 14 Advances in Mathematical Physics 13 Studies in Applied Mathematics 12 Computers & Mathematics with Applications 12 Theoretical and Mathematical Physics 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Reports on Mathematical Physics 9 Applicable Analysis 9 Abstract and Applied Analysis 9 Communications in Theoretical Physics 8 Chaos 8 Analysis and Mathematical Physics 7 Mathematical Methods in the Applied Sciences 7 Wave Motion 7 Journal of Nonlinear Science 7 International Journal of Nonlinear Sciences and Numerical Simulation 6 Journal of Differential Equations 6 Mathematical Problems in Engineering 6 International Journal of Geometric Methods in Modern Physics 5 Discrete Dynamics in Nature and Society 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Advances in Mathematics 4 Acta Mathematicae Applicatae Sinica. English Series 4 Discrete and Continuous Dynamical Systems 4 Mathematical Physics, Analysis and Geometry 4 Nonlinear Analysis. Real World Applications 4 Journal of Applied Mathematics 4 Advances in Difference Equations 4 Frontiers of Mathematics in China 4 Journal of Applied Analysis and Computation 4 East Asian Journal on Applied Mathematics 3 Communications in Mathematical Physics 3 International Journal of Theoretical Physics 3 Nonlinearity 3 Journal of Computational and Applied Mathematics 3 Physica D 3 Applied Mathematical Modelling 3 International Journal of Numerical Methods for Heat & Fluid Flow 2 Physica A 2 Reviews in Mathematical Physics 2 Journal of Functional Analysis 2 Monatshefte für Mathematik 2 Proceedings of the American Mathematical Society 2 Chinese Annals of Mathematics. Series B 2 Numerical Methods for Partial Differential Equations 2 International Journal of Computer Mathematics 2 Applied Mathematics. Series B (English Edition) 2 Journal of the Egyptian Mathematical Society 2 Complexity 2 Journal of Shanghai University 2 Boundary Value Problems 2 Complex Analysis and Operator Theory 2 Journal of Physics A: Mathematical and Theoretical 2 Journal of Function Spaces 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Modern Physics Letters A 1 Computers and Fluids 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Computational Physics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 International Journal of Mathematics and Mathematical Sciences 1 Mathematics and Computers in Simulation 1 Memoirs of the American Mathematical Society 1 Quaestiones Mathematicae 1 Results in Mathematics 1 Transactions of the American Mathematical Society 1 Applied Mathematics and Mechanics. (English Edition) 1 Acta Applicandae Mathematicae 1 Mathematical and Computer Modelling 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 NoDEA. Nonlinear Differential Equations and Applications 1 Advances in Differential Equations 1 Integral Transforms and Special Functions 1 Engineering Analysis with Boundary Elements 1 Journal of Difference Equations and Applications 1 European Journal of Control 1 Journal of the European Mathematical Society (JEMS) 1 Journal of High Energy Physics 1 Annales Henri Poincaré 1 International Journal of Modern Physics C 1 Journal of Modern Optics 1 Nonlinear Analysis. Modelling and Control 1 Communications on Pure and Applied Analysis 1 Analysis and Applications (Singapore) 1 Waves in Random and Complex Media 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Complex Variables and Elliptic Equations 1 Proyecciones ...and 9 more Serials
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#### Cited in 35 Fields

 531 Partial differential equations (35-XX) 448 Dynamical systems and ergodic theory (37-XX) 42 Algebraic geometry (14-XX) 35 Numerical analysis (65-XX) 29 Ordinary differential equations (34-XX) 26 Difference and functional equations (39-XX) 19 Quantum theory (81-XX) 17 Fluid mechanics (76-XX) 15 Computer science (68-XX) 15 Mechanics of particles and systems (70-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Nonassociative rings and algebras (17-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Special functions (33-XX) 8 Optics, electromagnetic theory (78-XX) 7 Approximations and expansions (41-XX) 4 Topological groups, Lie groups (22-XX) 4 Operator theory (47-XX) 4 Mechanics of deformable solids (74-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 General and overarching topics; collections (00-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Systems theory; control (93-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) 1 Geophysics (86-XX)